2 questions: 1 - what is wrong with the tip of my mesh? 2 - Why does the bevel modifier have 2 different effects?
Problem 1.

Sometimes a Mirror modifier enforces triangles in a mesh which can be removed after the modifier is applied. In this particular case, when the triangles are eventually removed, the pinch will go, too. (The surface isn't illustrated here, just the topology)



Problem 2.

The width of the bevel created by the Bevel modifier is not being defined by the modifier's 'Width' setting, but being limited in both meshes by the 'Clamp Overlap' constraint. That constraint is different in the two meshes. If you set the 'Width' of the Bevel to a much smaller number, say about 0.01, then you can achieve the same actual bevel width in each mesh, as on the left, below. 



If that width is not acceptable throughout your meshes, then you could, for example, make more selective Vertex Groups, and bevel to different degrees for each Group.